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Relevant bibliographies by topics / Fourier decomposition

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Academic literature on the topic 'Fourier decomposition'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Fourier decomposition"

1

Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also

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Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also

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3

Wang, Yanbo, and Tao Qian. "Adaptive Fourier decomposition in." Mathematical Methods in the Applied Sciences 42, no. 6 (2019): 2016–24. http://dx.doi.org/10.1002/mma.5494.

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4

ZHANG, LIMING, and HONG LI. "A NOVEL SIGNAL DECOMPOSITION APPROACH — ADAPTIVE FOURIER DECOMPOSITION." Advances in Adaptive Data Analysis 03, no. 03 (2011): 325–38. http://dx.doi.org/10.1142/s1793536911000702.

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This paper presents a novel signal decomposition approach — adaptive Fourier decomposition (AFD), which decomposes a given signal based on its physical characters. The algorithm is described in detail, that is based on recent theoretical studies on analytic instantaneous frequencies and stands as a realizable variation of the greedy algorithm. The principle of the algorithm gives rise to fast convergence in terms of energy. Effectiveness of the algorithm is evaluated by comparison experiments with the classical Fourier decomposition (FD) algorithm. The results are promising.

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Qian, Tao, Liming Zhang, and Zhixiong Li. "Algorithm of Adaptive Fourier Decomposition." IEEE Transactions on Signal Processing 59, no. 12 (2011): 5899–906. http://dx.doi.org/10.1109/tsp.2011.2168520.

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Kutay, M. Alper, Hakan Özaktaş, Haldun M. Ozaktas, and Orhan Arıkan. "The fractional Fourier domain decomposition." Signal Processing 77, no. 1 (1999): 105–9. http://dx.doi.org/10.1016/s0165-1684(99)00063-8.

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QIAN, TAO, and YANBO WANG. "REMARKS ON ADAPTIVE FOURIER DECOMPOSITION." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s0219691313500070.

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This is a continuation of the study of adaptive Fourier decomposition (AFD).15 Under a mild condition not in terms of smoothness, a convergence rate is provided. We prove that the selection of the parameters corresponding to Fourier series in the average sense is optimal. We also present the transformation matrices between the adaptive rational orthogonal system and the related sequence of the shifted Cauchy kernels and their derivatives.

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Qian, Tao. "Two-dimensional adaptive Fourier decomposition." Mathematical Methods in the Applied Sciences 39, no. 10 (2016): 2431–48. http://dx.doi.org/10.1002/mma.3649.

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Hansen, L., and J. O. Petersen. "Fourier Decomposition Parameters for the Halo RR Lyrae Variables U and V Caeli." International Astronomical Union Colloquium 82 (1985): 272–75. http://dx.doi.org/10.1017/s0252921100109509.

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AbstractUBVRI light curves are obtained for the two halo RR Lyrae variables U Caeli with period 0.420 days (73 observations) and V Caeli with period 0.571 days (42 observations). It is shown that their light curve characteristics are very similar to those of field RR Lyrae stars.Fourier decompositions are studied for all five magnitudes and the resulting amplitude ratios and phase differences are discussed. The differences in the Fourier decomposition parameters between the five magnitudes are shown to be relatively small. Comparisons of the Fourier decomposition parameters for the two halo RR

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Kožar, Ivica, Željko Jeričević, and Tatjana Pecak. "Approximate modal analysis using Fourier decomposition." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012119. http://dx.doi.org/10.1088/1757-899x/10/1/012119.

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Dissertations / Theses on the topic "Fourier decomposition"

1

Liu, Zhu Lin. "Speech synthesis via adaptive Fourier decomposition." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2493215.

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Li, Zhi Xiong. "A revision of adaptive Fourier decomposition." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2590642.

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Shi, Rong. "Applications of adaptive Fourier decomposition to financial data." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592936.

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Mai, Wei Xiong. "Time frequency distribution associated with adaptive Fourier decomposition and its variation." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2590643.

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Avetisyan, Zhirayr. "Mode decomposition and Fourier analysis of physical fields in homogeneous cosmology." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-107907.

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In this work the methods of mode decomposition and Fourier analysis of quantum fields on curved spacetimes previously available mainly for the scalar fields on Friedman-Robertson-Walker spacetimes are extended to arbitrary vector fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. Explicit constructions are performed for a variety of situations arising in homogeneous cosmology. A number of results concerning classical and quantum fields known for very restricte

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Blackburn, John William Teasdale. "High-resolution Fourier transform ion cyclotron resonance mass spectrometry and nuclear magnetic resonance spectroscopy of humic substances." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31149.

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Humic substances (HS) are described as a complex mixture of organic molecules formed by incomplete decomposition of plant, animal and microbial matter. They are found in soil, water and air and have many environmental roles, e.g. water retention and metal ion binding in soil. Despite their importance, the molecular composition of HS is poorly understood. This is mostly because of an inability to separate individual molecules from these complex mixtures and then characterise them by standard analytical methods such as NMR and MS. In order improve the understanding of these important mixtures I

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Liu, Xiaohua. "Anion-Peptide Adduct Formation and Decomposition As Studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) Mass Spectrometry." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/td/1748.

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A new “best match” match model has been developed to account for adduct formation on multiply charged peptides observed in negative ion electrospray mass spectrometry. To obtain a stable adduct, the model necessitates an approximate matching of apparent gas-phase basicity (GBapp) of a given proton bearing site on the peptide with the gas-phase basicity (GB) of the anion attaching at that site. Evidence supporting the model is derived from the fact that singly charged adducts were only observed for lower GB anions: HSO4-, I-, CF3COO-. Ions that have medium GBs (NO3-, Br-, H2PO4-) only form addu

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Workalemahu, Tsegaselassie. "Singular Value Decomposition in Image Noise Filtering and Reconstruction." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/52.

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The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image re

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Eliasson, Bengt. "Numerical Vlasov–Maxwell Modelling of Space Plasma." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2929.

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The Vlasov equation describes the evolution of the distribution function of particles in phase space (x,v), where the particles interact with long-range forces, but where shortrange "collisional" forces are neglected. A space plasma consists of low-mass electrically charged particles, and therefore the most important long-range forces acting in the plasma are the Lorentz forces created by electromagnetic fields. What makes the numerical solution of the Vlasov equation a challenging task is that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional

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Colom, i. Bernadich Miquel. "Measuring the Characteristic Sizes of Convection Structures in AGB Stars with Fourier Decomposition Analyses : the Stellar Intensity Analyzer (SIA) Pipeline." Thesis, Uppsala universitet, Teoretisk astrofysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414041.

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Context. Theoretical studies predict that the length scale of convection in stellar atmospheres isproportional to the pressure scale height, which implies that giant and supergiant stars should have convection granules of sizes comparable to their radii. Numerical simulations and the observation of anisotropies on stellar discs agree well with this prediction. Aims. To measure the characteristic sizes of convection structures of models simulated with the CO5BOLD code, to look at how they vary between models and to study their limitations due to numerical resolution. Methods. Fourier analyses a

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Books on the topic "Fourier decomposition"

1

Moin, Parviz. Characteristic eddy decomposition of turbulence in a channel. National Aeronautics and Space Administration, Ames Research Center, 1991.

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2

Golubov, B., V. Skvortsov, and A. Efimov. Walsh Series and Transforms: Theory and Applications. Springer Netherlands, 2012.

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3

Bisseling, Rob H. Parallel Scientific Computation. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788348.001.0001.

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This book explains how to use the bulk synchronous parallel (BSP) model to design and implement parallel algorithms in the areas of scientific computing and big data. Furthermore, it presents a hybrid BSP approach towards new hardware developments such as hierarchical architectures with both shared and distributed memory. The book provides a full treatment of core problems in scientific computing and big data, starting from a high-level problem description, via a sequential solution algorithm to a parallel solution algorithm and an actual parallel program written in the communication library B

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Time‒Frequency and Time‒Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling (Applied and Numerical Harmonic Analysis). Birkhäuser Boston, 2007.

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Book chapters on the topic "Fourier decomposition"

1

Roepstorff, Gert. "Fourier Decomposition." In Path Integral Approach to Quantum Physics. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57886-1_4.

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Chen, Hsin-Chu. "A Block Fourier Decomposition Method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48051-x_35.

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3

Zhou, Wei, Zhongren Feng, Y. F. Xu, Xiongjiang Wang, and Hao Lv. "Empirical Fourier Decomposition for Time-Domain Signal Decomposition." In Topics in Modal Analysis & Testing, Volume 8. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75996-4_8.

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He, Can, Liming Zhang, Xiangjian He, and Wenjing Jia. "A New Image Decomposition and Reconstruction Approach – Adaptive Fourier Decomposition." In MultiMedia Modeling. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14442-9_20.

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5

Petersen, J. O. "On the Application of Fourier Decomposition Parameters." In Nonlinear Phenomena in Stellar Variability. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1062-4_20.

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Tilmanne, Joelle, and Thierry Dutoit. "Stylistic Walk Synthesis Based on Fourier Decomposition." In Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03892-6_9.

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Simon, Norman R. "The Fourier Decomposition Technique: Interpreting the Variations of Pulsating Stars." In Pulsation and Mass Loss in Stars. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3029-2_2.

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8

Tan, Chunyu, Liming Zhang, and Tao Qian. "A New Supervised Learning Approach: Statistical Adaptive Fourier Decomposition (SAFD)." In Communications in Computer and Information Science. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-36802-9_42.

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Masliev, I. "Use of a Fourier Decomposition Technique in Aquatic Ecosystems Modelling." In Predictability and Nonlinear Modelling in Natural Sciences and Economics. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0962-8_34.

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Hussein, Hagar, Ashhadul Islam, and Samir Brahim Belhaouari. "Stress Detection Using Novel Time–Frequency Decomposition: Progressive Fourier Transform." In Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4876-1_16.

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Conference papers on the topic "Fourier decomposition"

1

Hassan, Umaisa, and Amit Singhal. "Neural Network-Based Schizophrenia Diagnosis Utilizing Fourier Decomposition." In 2024 Global Conference on Communications and Information Technologies (GCCIT). IEEE, 2024. https://doi.org/10.1109/gccit63234.2024.10862502.

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Long, Ruiqi, Hongyi Xie, and Defu Lian. "Time Series Forecasting with Multi-scale Decomposition and Fourier Neural Operators." In 2024 7th International Conference on Computer Information Science and Application Technology (CISAT). IEEE, 2024. http://dx.doi.org/10.1109/cisat62382.2024.10695364.

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Li, Hao, Ziyuan Zhan, Zhizhuo Zhang, Zhiming Yang, Liang Bao, and Mouxun Sun. "Modeling Method of Coaxial Cable Transmission Characteristics Based on Fourier Decomposition." In 2024 IEEE 2nd International Conference on Electrical, Automation and Computer Engineering (ICEACE). IEEE, 2024. https://doi.org/10.1109/iceace63551.2024.10898676.

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Shen, Jianhao, Daniel Donnelly, Asela Perera, and Swapnajit Chakravarty. "Phase-change-material integrated, phase-error corrected, resolution-enhanced Michelson Interferometer Fourier Transform Spectrometer." In CLEO: Science and Innovations. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_si.2024.sf2a.6.

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We experimentally demonstrate a hybrid silicon waveguide integrated with phase change materials to enable active phase error correction for spectral decomposition in compact on-chip Fourier Transform spectrometer based on spatially heterodyned array of Michelson interferometers.

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5

Mahato, Ashok, Shailesh Vitthalrao Bhalerao, Ram Bilas Pachori, Vikram M. Gadre, and Dipika Das Mahapatra. "Neurological Responses to Meditation with EEG Analysis Using Novel Empirical Fourier-Bessel Decomposition Approach." In 2025 10th International Conference on Signal Processing and Communication (ICSC). IEEE, 2025. https://doi.org/10.1109/icsc64553.2025.10968250.

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Ding, Hong, Chia Chao Kang, SuYang Xi, Zehang Liu, Xuan Zhang, and Yi Ding. "FPGA-Optimized Hardware Accelerator for Fast Fourier Transform and Singular Value Decomposition in AI." In 2024 International Conference on Computing Innovation, Intelligence, Technologies and Education (CIITE). IEEE, 2024. https://doi.org/10.1109/ciite62244.2024.10987675.

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Melli, F., K. Vasko, L. Rosa, F. Benabid, and L. Vincetti. "Transverse Roughness: Modeling and Effects Analysis on Inhibited Coupling Fibers." In Specialty Optical Fibers. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/sof.2024.som3f.6.

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A Transverse Roughness theoretical model based on the Azimuthal Fourier Decomposition is proposed to analyse the effects of this perturbation on the Confinement Loss of Hollow-Core Inhibited Coupling Fibers. Scaling laws are also given.

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Brault, Janes W., and Mark C. Abrams. "DECOMP: A Fourier Transfom Spectra Decomposition Program." In High Resolution Fourier Transform Spectroscopy. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/hrfts.1989.pdp2.

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Current techniques for processing high resolution Fourier transform spectra revolve around interactive graphical display of the spectrum on a computer. The DECOMP spectrum decomposition program is designed explicitly for the reduction of Fourier transform spectra and focuses on reducing a spectrum into a list of line parameters. Basic methods of spectrum manipulation will be demonstrated and a IBM PC - compatible computer will be available for hands-on demonstrations of the process of spectrum analysis. Figures 1 and 2 illustrate the process of background subtraction: in Figure 1 a low resolut

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Goyal, Navin, Santosh Vempala, and Ying Xiao. "Fourier PCA and robust tensor decomposition." In STOC '14: Symposium on Theory of Computing. ACM, 2014. http://dx.doi.org/10.1145/2591796.2591875.

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Borowicz, Adam. "GPU Implementation of Adaptive Fourier Decomposition." In 2019 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). IEEE, 2019. http://dx.doi.org/10.23919/spa.2019.8936752.

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